Instrument-free Identification and Estimation of Differentiated Products Models Using Cost Data

Abstract

We propose a new methodology for identifying and estimating demand in differentiated products models when demand and cost data are available. The method deals with the endogeneity of prices to demand shocks and the endogeneity of outputs to cost shocks by using cost data rather than instruments. Further, our methodology allows for unobserved market size. Based on our identification strategy, we develop a two-step Sieve Nonlinear Least Squares (SNLLS) estimator for the logit and BLP demand specifications and prove its identification, consistency and asymptotic normality. Using Monte Carlo experiments, we show that our method works well in contexts where commonly used instruments are correlated with demand and cost shocks and thus, biased. We also apply our method to the estimation of deposit demand in the US banking industry.

Keywords: Differentiated Goods Oligopoly, Instruments, Parametric Identification, Nonparametric Identification, Cost data

JEL Classification: C13, C18, L13, L41